The Labour leader's comments come as Farage defended controversial remarks that he would be concerned if a group of Romanians were to move in next door to him.
When asked whether UK Independence Party (Ukip) leader Farage was racist, Miliband told Sky's Dermot Murnaghan: "Personally, I don't think so.
"I think his remarks he made were deeply offensive ... I think they were a racial slur but I don't think of Nigel Farage as a racist himself."
Farage's party is widely expected to top the poll in Thursday's elections to the European Parliament.
During a bruising interview on LBC radio that was eventually interrupted by his spin doctor, the Ukip leader was repeatedly challenged over recent comments that he felt ''uncomfortable'' hearing so many foreign languages spoken on trains in London.
Asked whether he was uncomfortable when his wife Kirsten and their daughters spoke German, Farage replied: ''No, because they can speak English.''
Pressed again on the issue, he said: ''I don't suppose she speaks it on the train.''
Farage was also pressed on his suggestion that he would feel uncomfortable if Romanians moved in next door.
''If you lived in London, I think you would be,'' he said.
Interviewer James O'Brien asked: ''What about if a group of German children did? What's the difference?
''You know what the difference is,'' Farage said.
In a statement, the Ukip leader said: ''The unfortunate reality is that we are in a political union with a post-Communist country that has become highly susceptible to organised crime.
''Where there are differential crime rates between nationalities, it is perfectly legitimate to point this out and to discuss it in the public sphere, and I shall continue to do so.
''Police figures are quite clear that there is a high level of criminality within the Romanian community in Britain. This is not to say for a moment that all or even most Romanian people living in the UK are criminals.
''But it is to say that any normal and fair-minded person would have a perfect right to be concerned if a group of Romanian people suddenly moved in next door.
''So far as I can see most of those media commentators objecting to this statement are people living in million pound houses for whom the prospect of such a turn of events is not a real one.''